Ribbon 2-knot groups of Coxeter type
Geometric Topology
2023-09-13 v1
Abstract
Wirtinger presentations of deficiency 1 appear in the context of knots, long virtual knots, and ribbon 2-knots. They are encoded by (word) labeled oriented trees and, for that reason, are also called LOT presentations. These presentations are a well known and important testing ground for the validity (or failure) of Whitehead's asphericity conjecture. In this paper we define LOTs of Coxeter type and show that for every given there exists a (prime) LOT of Coxeter type with group of rank . We also show that label separated Coxeter LOTs are aspherical.
Cite
@article{arxiv.2103.01987,
title = {Ribbon 2-knot groups of Coxeter type},
author = {Jens Harlander and Stephan Rosebrock},
journal= {arXiv preprint arXiv:2103.01987},
year = {2023}
}